Closed geodesics in simply connected Riemannian spaces of negative curvature
type: Item
instance of: scholarly article
title: Closed geodesics in simply connected Riemannian spaces of negative curvature
zbMATH Open document ID: 0960.53025
DOI: 10.1007/BF02674743
author: V. K. Ionin
published in: Siberian Mathematical Journal
publication date: 2001-02-12T00:00:00Z
full work available at URL: https://eudml.org/doc/120932
review text: It is known that if a Riemannian variety of negative sectional curvature is homeomorphic to the 2-dimensional plane then there is no closed geodesic on this variety. Examples are known of Riemannian varieties of negative sectional curvature which are homeomorphic to \(\mathbb R^n\), \(n>2\), and have closed geodesics. In the article under review, the author obtains Riemannian varieties with sectional curvature \(\leq -1\) which are diffeomorphic to \(\mathbb R^n\) and have closed geodesics.
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C21
zbMATH DE Number: 1564019
zbMATH Keywords: closed geodesic
zbMATH Keywords: Riemannian variety
zbMATH Keywords: negative sectional curvature
MaRDI profile type: Publication
Wikidata QID: Q115391896
cites work: Q5674032
cites work: Manifolds of Negative Curvature
OpenAlex ID: W2093763791
description: scientific article; zbMATH DE number 1564019